To solve the equation \(5x + 8 + x = 32\), we will follow these steps:
Step 1: Combine like terms
First, combine the \(x\) terms on the left side of the equation:
\[ 5x + x = 6x \]
So the equation becomes:
\[ 6x + 8 = 32 \]
Step 2: Isolate the variable term
Next, we want to isolate the term with \(x\). We do this by subtracting 8 from both sides of the equation:
\[ 6x + 8 - 8 = 32 - 8 \]
This simplifies to:
\[ 6x = 24 \]
Step 3: Solve for \(x\)
Now, we divide both sides by 6 to solve for \(x\):
\[ x = \frac{24}{6} = 4 \]
Solution
Thus, the solution to the equation is:
\[ x = 4 \]
Step 4: Check the solution
To check our solution, we will substitute \(x = 4\) back into the original equation:
Original equation:
\[ 5x + 8 + x = 32 \]
Substituting \(x = 4\):
\[ 5(4) + 8 + 4 = 32 \]
Calculating the left side:
\[ 20 + 8 + 4 = 32 \] \[ 32 = 32 \]
Since both sides of the equation are equal, our solution \(x = 4\) is verified.
Conclusion
The solution to the equation \(5x + 8 + x = 32\) is:
\[ \boxed{4} \]